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Existence, uniqueness and approximation for L p solutions of reflected BSDEs with generators of one-sided Osgood type

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Abstract

We prove several existence and uniqueness results for L p (p > 1) solutions of reflected BSDEs with continuous barriers and generators satisfying a one-sided Osgood condition together with a general growth condition in y and a uniform continuity condition or a linear growth condition in z. A necessary and sufficient condition with respect to the growth of barrier is also explored to ensure the existence of a solution. And, we show that the solutions may be approximated by the penalization method and by some sequences of solutions of reflected BSDEs. These results are obtained due to the development of those existing ideas and methods together with the application of new ideas and techniques, and they unify and improve some known works.

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Acknowledgements

The author would like to thank the anonymous referee for his/her careful reading and helpful suggestions.

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Authors and Affiliations

  1. School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, P. R. China

    Sheng Jun Fan

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  1. Sheng Jun Fan
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Correspondence to Sheng Jun Fan.

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Supported by National Natural Science Foundation of China (Grant No. 11371362) and the Fundamental Research Funds for the Central Universities (Grant No. 2012QNA36)

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Fan, S.J. Existence, uniqueness and approximation for L p solutions of reflected BSDEs with generators of one-sided Osgood type. Acta. Math. Sin.-English Ser. 33, 807–838 (2017). https://doi.org/10.1007/s10114-016-6281-x

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  • DOI: https://doi.org/10.1007/s10114-016-6281-x

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